Embodiments of the invention relate generally to semiconductor devices and, more particularly, to the modeling of random dopant fluctuations (RDFs) in semiconductor devices.
The scaling of semiconductor devices, including complimentary metal-oxide-semiconductor (CMOS) devices, makes the electrical performance of a device more strongly dependent upon fluctuations in dopant distribution. In addition, lightly doped semiconductor device layers are inherently more susceptible to fluctuations in dopant distribution than are more heavily doped layers. For example, FinFETs benefit from lightly doped channels having dopant concentrations of around 1×1015 atoms per cubic centimeter. Similarly, SRAM and eDRAM devices typically have dopant concentrations between about 1×1016 and about 5×1018 atoms per cubic centimeter.
Random dopant fluctuations (RDFs) in such lightly doped device layers can dramatically affect device performance, making accurate modeling of RDFs important in quality control. Current RDF modeling techniques are only useful where dopant concentrations are about 5×1017 atoms per cubic centimeter or greater.
Poisson distribution statistics allow for discrete probabilistic counting of dopants if the average likelihood of finding a dopant atom is known. However, at low doping concentrations, the average likelihood is also low and the resulting probabilistic counting does not accurately model the actual doping distribution. In other words, a relatively large volume with a low dopant concentration results in a low probability of finding a dopant atom at any particular point within the volume, resulting in a model that artificially underestimates the dopant concentration and/or does not accurately model dopant distribution.